Need help taking the derivative of these 2 equations

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Need help taking the derivative of these 2 equations

sx+t

sx^3+x+2t


for the first i believe its
y` = s

for the second i am not sure if its but i believe its the first one

y` = 3sx^2+1

or

y` = 3sx^2+1+2


is this correct? the second one is kind of throwing me off with the b
 
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noname1 said:
Need help taking the derivative of these 2 equations

sx+t

sx^3+x+2t

With respect to which variable? s, x, or t?
 


to x, s and t are constants
 


noname1 said:
Need help taking the derivative of these 2 equations

sx+t

sx^3+x+2t
First off, these aren't equations. They are just expressions.
noname1 said:
for the first i believe its
y` = s
Yes.
noname1 said:
for the second i am not sure if its but i believe its the first one

y` = 3sx^2+1
Yes.
noname1 said:
or
No. From what you said in a later post, s and t are constants, so d/dx(t) = 0.
noname1 said:
y` = 3sx^2+1+2


is this correct? the second one is kind of throwing me off with the b
What b?
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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